It is the circular path of water in its various phases that gives the hydrological cycle its term cycle. The cycle begins with evaporation (from the ocean say), follows through condensation as clouds...
The carbon cycle is the cycle in which carbon moves around...well, here's a "simple" description: Humans take in oxygen and change it to carbon dioxide. Burning things and the fire itself, also...
Both of them are different, so both cycles work together. The carbon cycle lets out carbon dioxide and it then transfers it into the trees. The trees get the nitrogen and the cycle starts again.
Carbon Cycle: CO2 in the air get taken in by plants through photosynthesis. Carbon is in plant. Animals eat the plant. Carbon is in animal. Animal droppings contain carbon. Decomposers break down...